Standing to definitions :
A fact is a sentence that states that a relation holds between individuals. A rule is a relation that holds between individuals provided that some other relations hold.
According to this, why it is not possible to construct contradictory descriptions using facts and rules ?
For example, i can use as facts the fact that a = b and a = not(b) and i have a contradiction....
On
Who on earth says "A fact is a sentence that states that a relation holds between individuals"?
At least in my neck of the woods, there are two common views about facts -- namely that facts are true propositions (true declarative sentences), or that facts are truth-makers, the sort of thing that makes a true proposition true. But on either view, truth comes into it! A sentence that states that a relation between individuals can be false, and so is neither a fact-qua-true-sentence, nor does it correspond to a fact-qua-truth-maker.
You define a fact as an expression that says that some relation holds ... as such you can only express positive claims, and not any negations, i.e. you cannot express that some relation does not hold. The same is true for the rules: they apparently can only say that some relation holds when other relations holds, and so you cannot make any negations part of rules either. It is therefore impossible to use that $a \not = b$ as a fact, or make that part of a rule. And indeed, without negations you cannot get any contradictions at all.